Michael J. answered • 07/12/16

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You probably asked this question because the terminology "breadth" confused you. This means width of rectangle. Why couldn't the textbook use a simple term such as "width", which everyone knows well? Don't ask me. Ask the complicated developers of the textbook. Well anyway, here is how you solve the problem.

First define variables for the rectangle's dimensions.

Dimensions of the original rectangle:

Let width = x

Let length = x + 7

Dimensions of new rectangle:

width = x + 3

length = (x + 7) - 4 = x + 3

Now using these variables, we create equations to represent the areas of the rectangle accordingly. You know the area of rectangle is length times width.

Equate the original area to the new area.

x(x + 7) = (x + 3)(x + 3)

Solve this equation for x.

x

^{2 }+ 7x = x^{2}+ 6x + 9Subtracting x

^{2}on both sides,7x = 6x + 9

Subtracting 6x on both sides,

x = 9

Then all you have to do is substitute this value of x into the original dimensions.